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Khan Academy Donate [? ElizabethB Distribute to create an equivalent expression with the fewest symbols possible. (1)/(3)(3j+6)= Report a problem

Distribute to create an equivalent expression with the fewest symbols possible.\newline(13)(3j+6)=(\frac{1}{3})(3j+6)=\newline

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Power of a power: integer basesright chevron icon

Full solution

Q. Distribute to create an equivalent expression with the fewest symbols possible.\newline(13)(3j+6)=(\frac{1}{3})(3j+6)=\newline
  1. Factor Common Factor: Factor out the common factor in the expression (3j+6)(3j+6).\newlineIdentify the common factor in the terms 3j3j and 66.\newlineCommon factor: 33\newline(3j+6)(3j+6) can be factored as 3(j+2)3(j+2).
  2. Rewrite Using Factored Form: Rewrite the original expression using the factored form of (3j+6)(3j+6).13(3j+6)\frac{1}{3}(3j+6) becomes 13×13(j+2)\frac{1}{3} \times \frac{1}{3(j+2)}.
  3. Simplify by Combining Constants: Simplify the expression by combining the constants. 13×13(j+2)\frac{1}{3} \times \frac{1}{3(j+2)} simplifies to 13×3×1j+2\frac{1}{3\times3} \times \frac{1}{j+2}.
  4. Calculate Product of Constants: Calculate the product of the constants. \newline3×33 \times 3 equals 99.\newlineSo, 13×3\frac{1}{3 \times 3} simplifies to 19\frac{1}{9}.
  5. Combine Simplified Constant: Combine the simplified constant with the variable part of the expression.\newlineThe final expression is (1)/(9)×1j+2(1)/(9) \times \frac{1}{j+2}, which simplifies to (1)/(9(j+2))(1)/(9(j+2)).

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